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164 Reverse Engineering – Recent Advances and Applications Pietà composed of 14M triangle mesh generated from more than 700 scans (Bernardini et al., 1999), reconstruction of “Pisa Cathedral” (Pisa, Italy) from laser scans with over 154M samples (Cuccuru et al., 2009), and head and cerebral structures (hidden) extracted from 150 MRI slices using the marching cubes algorithm (about 150,000 triangles), as shown in Fig. 3. Fig. 3. Sample projects of scanning and triangulation, (a) Michelangelo’s Florentine Pietà, (b) Pisa Cathedral, and (c) head and cerebral structures Although many triangulation algorithms exist, they are not all fool-proof. They tend to generate meshes with a high triangle count. In addition, these algorithms implicitly assume topology of the shape to be reconstructed from triangulation, and the parameter settings often influences results and stability. A few mesh postprocessing algorithms, such as decimation (for examples, Schroeder, 1997; Hoppe et al., 1993), and mesh smoothness (e.g., Hansen et al., 2005; Li et al., 2009), are worthwhile mentioning for interested readers. 3.2 Segmentation One of the most important steps in shape engineering is mesh segmentation. Segmentation groups the original data points or mesh into subsets each of which logically belongs to a single primitive surface. In general, segmentation is a complex process. Often iterative region growing techniques are applied (Besl & Jain, 1988; Alrashdan et al., 2000; Huang & Meng, 2001). Some use noniterative methods, called direct segmentation (Várady et al., 1998), that are more efficient. In general, the segmentation process, such as (Vanco & Brunnett, 2004) involves a fast algorithm for k-nearest neighbors search and an estimate of first- and second-order surface properties. The first-order segmentation, which is based on normal vectors, provides an initial subdivision of the surface and detects sharp edges as well as flat or highly curved areas. The second-order segmentation subdivides the surface according to principal curvatures and provides a sufficient foundation for the classification of simple algebraic surfaces. The result of the mesh segmentation is subject to several important parameters, such as the k value (number of neighboring points chosen for estimating surface properties), and prescribed differences in the normal vectors and curvatures (also called sensitivity thresholds) that group the data points or mesh. As an example shown in Fig. 4a, a high sensitive threshold leads to scattered regions of small sizes, and a lower sensitive threshold tends to generate segmented regions that closely resemble the topology of the object, as illustrated in Fig. 4b. Most of the segmentation algorithms come with surface fitting, which fits a best primitive surface of appropriate type to each segmented region. It is important to specify a hierarchy of surface types in the order of geometric complexity, similar to that of Fig. 5 (Várady et al., 1997). In general, objects are bounded by relatively large primary (or functional) surfaces.
A Review on Shape Engineering and Design Parameterization in Reverse Engineering The primary surfaces may meet each other along sharp edges or there may be secondary or blending surfaces which may provide smooth transitions between them. Fig. 4. Example of mesh segmentation, (a) an object segmented into many small regions due to a high sensitivity threshold, and (b) regions determined with a low sensitivity threshold Fig. 5. A hierarchy of surfaces As discussed above, feature-based segmentation provides a sufficient foundation for the classification of simple algebraic surfaces. Algebraic surfaces, such as planes, natural quadrics (such as sphere, cylinders, and cones), and tori, are readily to be fitted to such regions. Several methods, including (Marshall et al., 2004), have been proposed to support such fitting, using least square fitting. In addition to primitive algebraic surfaces, more general surfaces with a simple kinematic generation, such as sweep surfaces, revolved surfaces (rotation sweep), extrusion surfaces (translation sweep), pipe surfaces, are directly compatible to CAD models. Fitting those surfaces to segmented data points or mesh is critical to the reconstruction of surface models and support of parameterization (Lukács et al., 1998). In some applications, not all segmented regions can be fitted with primitives or CADcompatible surfaces within prescribed error margin. Those remaining regions are classified as freeform surfaces, where no geometric or topological regularity can be recognized. These can be a collection of patches or possibly trimmed patches. They are often fitted with NURB surfaces. Many algorithms and methods have been proposed to support NURB surface fitting, such as (Tsai et al., 2009). 3.3 Solid modeling Solid modeling is probably the least developed in the shape engineering process in support of reverse engineering. Boundary representation (B-rep) and feature-based are the two basic representations for solid models. There have been some methods, such as (Várady et al., 1998), proposed to automatically construct B-rep models from point clouds or triangular mesh. Some focused on manufacturing feature recognition for process planning purpose, 165
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REVERSE ENGINEERING - RECENT ADVANC
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Contents Preface IX Part 1 Software
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Preface Introduction In the recent
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Preface XI and con’s related to t
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Preface XIII the step-by-step appli
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Part 1 Software Reverse Engineering
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4 Reverse Engineering - Recent Adva
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10 Reverse Engineering - Recent Adv
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58 2. Model driven architecture: An
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62 Fig. 1. Model, metamodels and tr
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100 Reverse Engineering - Recent Ad
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108 Table 1. Number of smoothers an
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238 5. Summary and discussions Reve
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268 Fig. 6. A closed polygon mesh r
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272 3. Results Reverse Engineering
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